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A fuzzy graph theoretic approach to face shape recognition using cubic outerplanar structures.

Deivanai Jaisankar1, Sujatha Ramalingam2, Gizachew Bayou Zegeye3

  • 1Mathematics, School of Science and Humanities, Shiv Nadar University Chennai, Rajiv Gandhi Salai (OMR), Kalavakkam, Chengalpattu District, Chennai, Tamil Nadu, 603110, India.

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Summary

Cubic fuzzy graphs enhance planarity analysis by managing uncertainty in vertex and edge membership. This research explores cubic fuzzy outerplanar graphs and their application in facial recognition.

Keywords:
Cubic fuzzy dual graphCubic fuzzy graphCubic fuzzy outerplanar graphFace shape recognitionMaximum and maximal vertex and edge deletion cubic fuzzy outerplanar subgraphsVertex and edge deletion cubic fuzzy outerplanar subgraphs

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Area of Science:

  • Graph Theory
  • Fuzzy Mathematics
  • Computer Science

Background:

  • Traditional graph planarity is extended to fuzzy frameworks.
  • Cubic fuzzy graphs (CuFGs) utilize cubic multisets to represent vagueness in membership.
  • CuFGs outperform interval valued and fuzzy graphs in managing uncertainty.

Purpose of the Study:

  • Investigate properties of cubic fuzzy outerplanar graphs.
  • Define and explore cubic fuzzy dual graphs.
  • Demonstrate practical applications in face recognition.

Main Methods:

  • Analysis of cubic fuzzy outerplanar graph properties.
  • Construction of subgraphs by vertex/edge removal.
  • Definition and exploration of cubic fuzzy dual graphs.

Main Results:

  • Characterization of cubic fuzzy outerplanar graphs.
  • Identification of maximal and maximum cubic fuzzy outerplanar subgraphs.
  • Establishment of relationships among cubic fuzzy dual graphs.

Conclusions:

  • Cubic fuzzy graphs provide a robust framework for modeling uncertainty.
  • The study advances graph theory with fuzzy concepts.
  • CuFGs show promise for accurate biometric identification, particularly in face recognition.